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JEE Main & Advanced Physics Kinetic Theory of Gases Question Bank Self Evaluation Test - Kinetic Theory

  • question_answer
    Two thermally insulated vessels 1 and 2 are filled with air at temperatures \[\] volume \[({{V}_{1}},\text{ }{{\text{V}}_{2}})\]and pressure \[({{P}_{1}},\text{ }{{\text{P}}_{2}})\] respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be

    A) \[{{T}_{1}}+{{T}_{2}}\]

    B) \[({{T}_{1}}+{{T}_{2}})/2\]

    C) \[\frac{{{T}_{1}}{{T}_{2}}\left( {{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}} \right)}{{{P}_{1}}{{V}_{1}}{{T}_{2}}+{{P}_{2}}{{V}_{2}}{{T}_{1}}}\]

    D) \[\frac{{{T}_{1}}{{T}_{2}}\left( {{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}} \right)}{{{P}_{1}}{{V}_{1}}{{T}_{1}}+{{P}_{2}}{{V}_{2}}{{T}_{2}}}\]

    Correct Answer: C

    Solution :

    [c] \[\frac{P({{V}_{1}}+{{V}_{2}})}{T}=\frac{{{P}_{1}}{{V}_{1}}}{{{T}_{1}}}+\frac{{{P}_{2}}{{V}_{2}}}{{{T}_{2}}}\]                       ?.(i) Also \[P({{V}_{1}}+{{V}_{2}})\,={{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}}\]                      ?(ii) After solving above equations, we get \[T=\left[ \frac{\left( {{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}} \right){{T}_{1}}{{T}_{2}}}{{{P}_{1}}{{V}_{1}}T+{{P}_{2}}{{V}_{2}}{{T}_{2}}} \right]\]


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